What is the rule of thumb for number of servers to synchronize to?
It is entirely up to you and your tolerance for outages. Obviously you have some tolerance, or you would be buying GPS receivers and installing your own stratum-1 servers. But three is a good place to start, and you can progress to three-groups-of-three if you feel the need. Remember that network outages are at least as likely as timeserver outages, so if you only have one network path to the outside world then adding a lot more timeservers doesn’t really improve your reliability (your ISP is the single-point-of-failure).